US10515161B1ActiveUtility
Transient blade row flow modeling with profile-transformation pitch-change model and harmonic solution method
Est. expiryMay 15, 2035(~8.8 yrs left)· nominal 20-yr term from priority
G06F 2111/10G06F 30/28G06F 30/23F05D 2260/81G06F 30/20G06F 2217/16G06F 17/5009
59
PatentIndex Score
1
Cited by
6
References
24
Claims
Abstract
Systems and methods are provided for modeling fluid flow in a turbomachine. A specification of a system including at least a stator and a rotor of a turbomachine is received. The stator is coupled to the rotor via a profile-transformation (PT) interface. A flow profile for fluid flow across the PT interface is expanded or compressed based on a pitch ratio between the stator and the rotor. Flow variables of governing flow equations for the fluid flow in the system are represented as a Fourier series with spatially-varying Fourier coefficients. The Fourier series representation is substituted into the governing flow equations to obtain a modified form of the governing flow equations. The modified form of the governing flow equations is solved using a steady-state solution method to model the fluid flow in the system. The modeling utilizes an implicit solution discretization across the PT interface.
Claims
exact text as granted — not AI-modifiedIt is claimed:
1. A computer-implemented method of modeling fluid flow in blade rows of a turbomachine, the method comprising:
receiving a specification of a physical system including at least a first stator and a rotor of a turbomachine, wherein
the first stator and the rotor are coupled via a first profile-transformation (PT) interface according to a profile-transformation pitch-change technique, wherein a flow profile for fluid flow across the first PT interface is expanded or compressed based on a pitch ratio between the first stator and the rotor;
representing fluid flow in the physical system according to a Fourier series with spatially-varying Fourier coefficients, the Fourier series including one or more terms that are based on the rotor's passing frequency; and
determining the fluid flow in the physical system by an implicit solution discretization across the first PT interface,
wherein the fluid flow in the physical system is determined based on a modified form of governing flow equations for the fluid flow in the physical system, the modified form of the governing flow equations including a pseudo-time term, the modified form of the governing flow equations corresponding to a substitution of the Fourier series into the governing flow equations, and wherein the determining comprises solving the modified form of the governing flow equations using a steady-state solution method.
2. The computer-implemented method of claim 1 ,
wherein (i) the representing fluid flow in the physical system according to the Fourier series, (ii) the substitution of the Fourier series representation into the governing flow equations, and (iii) the introducing of the pseudo-time term comprise steps of a harmonic analysis technique, the harmonic analysis technique enabling the governing flow equations to be solved using a solution strategy that includes terms in a time domain and terms in a frequency domain.
3. The computer-implemented method of claim 2 , wherein the harmonic analysis technique is a single-frequency harmonic analysis based on the rotor's passing frequency.
4. The computer-implemented method of claim 1 , wherein the Fourier series includes the one or more terms that are based on the rotor's passing frequency and does not include terms that are based on other frequencies.
5. The computer-implemented method of claim 1 , wherein the profile-transformation pitch-change technique is fully implicit (i) at periodic boundaries of the physical system, and (ii) at the first PT interface between the first stator and the rotor.
6. The computer-implemented method of claim 1 , wherein the profile-transformation pitch-change technique (i) does not include Fourier-based approximations at periodic boundaries of the physical system, and (ii) does not include Fourier-based approximations at the first PT interface between the first stator and the rotor.
7. The computer-implemented method of claim 1 , wherein the physical system includes at least the first stator, the rotor, and a second stator, the method further comprising:
coupling the rotor to the second stator via a second PT interface, wherein a flow profile for fluid flow across the second PT interface is expanded or compressed based on a pitch ratio between the rotor and the second stator, and
wherein the implicit solution discretization occurs across (i) the first PT interface, and (ii) the second PT interface.
8. The computer-implemented method of claim 7 , wherein the Fourier series includes the one or more terms that are based on the rotor's passing frequency and does not include terms that are based on other frequencies.
9. The computer-implemented method of claim 7 , wherein in the profile-transformation pitch-change technique, geometries of the first stator, the rotor, and the second stator are not scaled or altered.
10. The computer-implemented method of claim 7 , wherein the profile-transformation pitch-change technique is fully implicit (i) at periodic boundaries of the physical system, (ii) at the first PT interface between the first stator and the rotor, and (iii) at the second PT interface between the rotor and the second stator.
11. The computer-implemented method of claim 7 ,
wherein in the profile-transformation pitch-change technique, a monitor point located in the first stator, the rotor, or the second stator senses only the rotor's passing frequency.
12. The computer-implemented method of claim 1 , wherein in the profile-transformation pitch-change technique, when the rotor moves a distance equal to a pitch of the rotor, the first stator coupled to the rotor via the first PT interface senses one full passing of the rotor, independent of the pitch ratio between the first stator and the rotor.
13. The computer-implemented method of claim 1 , wherein M harmonics are retained in the Fourier series and (2M+1) Fourier coefficients are retained for each flow variable, the method further comprising:
determining the (2M+1) Fourier coefficients for each flow variable based on a knowledge of a temporal behavior of the flow variables at (2M+1) equally-spaced points in time over a period T, wherein the period T is a period of the blade passing.
14. The computer-implemented method of claim 13 , wherein the modified form of the governing flow equations is a pseudo-time harmonic balance equation, the method further comprising:
generating (2M+1) computational grids, wherein each of the computational grids is associated with one of the (2M+1) equally-spaced points in time;
at each node of the (2M+1) computational grids, storing values of one or more of the flow variables;
discretizing the pseudo-time harmonic balance equation across the (2M+1) computational grids using a computational fluid dynamics (CFD) technique; and
solving the pseudo-time harmonic balance equation across the (2M+1) computational grids using computer-based numerical calculations, wherein the solving of the pseudo-time harmonic balance equation includes the determining of the (2M+1) Fourier coefficients for each flow variable.
15. The computer-implemented method of claim 1 ,
wherein a pitch of the first stator is not equal to a pitch of the rotor, and
wherein the profile-transformation pitch-change technique enables the fluid flow in the physical system to be modeled using a single blade passage or few blade passages per blade row of the physical system.
16. The computer-implemented method of claim 1 ,
wherein in the profile-transformation pitch-change technique, a monitor point located in the first stator, the second stator, or the rotor senses only the rotor's passing frequency and harmonics of the rotor's passing frequency.
17. The computer-implemented method of claim 1 ,
wherein the Fourier series approximates flow variations in the fluid flow as harmonics of a fundamental frequency, and wherein the harmonics are substituted into the governing flow equations.
18. The computer-implemented method of claim 1 , wherein the governing flow equations are Euler equations or Navier-Stokes equations.
19. The computer-implemented method of claim 1 , wherein the governing flow equations are represented as
∂
Q
∂
t
+
∂
E
∂
x
+
∂
G
∂
y
=
0
,
where Q is a conservative solution vector, E and G are flux vectors, and physical coordinates of the physical system include spatial coordinates x and y and temporal coordinate t.
20. The computer-implemented method of claim 19 , wherein the representing of the flow variables as the Fourier series comprises:
rewriting the governing flow equations in a semi-discrete form as
∂
Q
∂
t
=
-
R
(
Q
)
,
wherein the Fourier series comprises
Q
j
=
Q
^
j
0
+
∑
m
=
1
M
Q
^
j
mc
Cos
(
m
ω
t
)
+
∑
m
=
1
M
Q
^
j
ms
Sin
(
m
ω
t
)
,
R
j
=
R
^
j
0
+
∑
m
=
1
M
R
^
j
mc
Cos
(
m
ω
t
)
+
∑
m
=
1
M
R
^
j
ms
Sin
(
m
ω
t
)
,
where M is a number of harmonics retained in the Fourier series representation, ω is the angular frequency due to blade passing, {circumflex over (Q)} j mc or and {circumflex over (Q)} j ms are the cosine and sine of Fourier coefficient for the flow variable Q j at mesh location j, and {circumflex over (R)} j mc and {circumflex over (R)} j ms are the cosine and sine of the Fourier coefficient for the residual term R j at the mesh location j.
21. The computer-implemented method of claim 20 , wherein the substitution of the Fourier series into the governing flow equations comprises:
substituting flow harmonics of the Fourier series into the governing flow equations followed by Discrete Inverse Fourier Transform (DIFT) to put the equation back in the time-domain and obtain the modified form of the governing flow equations represented as
[ P ]{ {tilde over (Q)} j }+{{tilde over (R)} j }={0}, Equation 5
where matrix [P] contains the time spectral operator coupling all (2M+1) time levels together, {{tilde over (Q)} j } is a vector of conservation variables at (2M+1) equally-spaced points in time over one temporal period T, the period T being a period of the blade passing, {{tilde over (R)} j } is a vector of flux variables at the (2M+1) equally-spaced points in time over the one temporal period T, and
ω
=
2
π
T
.
22. The computer-implemented method of claim 21 , wherein the introducing of the pseudo-time term into the modified form of the governing flow equations yields the form of the equations capable of being solved using the steady-state solution method:
∂
{
Q
~
j
}
∂
τ
+
[
P
]
{
Q
~
j
}
+
{
R
~
j
}
=
0
,
where
∂
{
Q
~
j
}
∂
τ
is the pseudo-time term including a fictitious time τ used to march the solution to a steady state by driving the pseudo-time term to zero.
23. A system for modeling fluid flow in blade rows of a turbomachine, the system comprising:
a processing system; and
a memory in communication with the processing system, wherein the processing system is configured to execute steps comprising:
receiving a specification of a physical system including at least a first stator and a rotor of a turbomachine, wherein
the first stator and the rotor are coupled via a first profile-transformation (PT) interface according to a profile-transformation pitch-change technique, wherein a flow profile for fluid flow across the first PT interface is expanded or compressed based on a pitch ratio between the first stator and the rotor;
representing fluid flow in the physical system according to a Fourier series with spatially-varying Fourier coefficients, the Fourier series including one or more terms that are based on the rotor's passing frequency;
and
determining the fluid flow in the physical system by an implicit solution discretization across the first PT interface,
wherein the fluid flow in the physical system is determined based on a modified form of governing flow equations for the fluid flow in the physical system, the modified form of the governing flow equations including a pseudo-time term, the modified form of the governing flow equations corresponding to a substitution of the Fourier series into the governing flow equations, and wherein the determining comprises solving the modified form of the governing flow equations using a steady-state solution method.
24. A non-transitory computer-readable storage medium for modeling fluid flow in blade rows of a turbomachine, the computer-readable storage medium comprising computer-executable instructions which, when executed, cause a processing system to execute steps comprising:
receiving a specification of a physical system including at least a first stator and a rotor of a turbomachine, wherein
the first stator and the rotor are coupled via a first profile-transformation (PT) interface according to a profile-transformation pitch-change technique, wherein a flow profile for fluid flow across the first PT interface is expanded or compressed based on a pitch ratio between the first stator and the rotor;
representing fluid flow in the physical system according to a Fourier series with spatially-varying Fourier coefficients, the Fourier series including one or more terms that are based on the rotor's passing frequency;
and
determining the fluid flow in the physical system by an implicit solution discretization across the first PT interface,
wherein the fluid flow in the physical system is determined based on a modified form of governing flow equations for the fluid flow in the physical system, the modified form of the governing flow equations including a pseudo-time term, the modified form of the governing flow equations corresponding to a substitution of the Fourier series into the governing flow equations, and wherein the determining comprises solving the modified form of the governing flow equations using a steady-state solution method.Cited by (0)
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